# NAME

Algorithm::CP::IZ - Perl interface for iZ-C library

# SYNOPSIS

``````  use Algorithm::CP::IZ;

my \$iz = Algorithm::CP::IZ->new();

my \$v1 = \$iz->create_int(1, 9);
my \$v2 = \$iz->create_int(1, 9);
\$iz->Add(\$v1, \$v2)->Eq(12);
my \$rc = \$iz->search([\$v1, \$v2]);

if (\$rc) {
print "ok\n";
print "v1 = ", \$v1->value, "\n";
print "v2 = ", \$v2->value, "\n";
}
else {
print "fail\n";
}``````

# DESCRIPTION

Algorithm::CP::IZ is a simple interface of iZ-C constraint programming library.

Functions declared in iz.h are mapped to:

methods of Algorithm::CP::IZ

initialize, variable constructor, most of constraints and search related functions

methods of Algorithm::CP::IZ::Int

accessors of variable attributes and some relationship constraints

Please refer to iZ-C reference manual to see specific meaning of methods.

## SIMPLE CASE

In most simple case, this library will be used like following steps:

``````  # initialize
use Algorithm::CP::IZ;
my \$iz = Algorithm::CP::IZ->new();

# construct variables
my \$v1 = \$iz->create_int(1, 9);
my \$v2 = \$iz->create_int(1, 9);

# add constraints ("v1 + v2 = 12" in this case)
\$iz->Add(\$v1, \$v2)->Eq(12);

# search solution
my \$rc = \$iz->search([\$v1, \$v2]);

# you may get "v1 = 3, v2 = 9"
print "v1 = \$v1, v2 = \$v2\n";``````

# CONSTRUCTOR

new

Initialize iZ-C library (cs_init is called). For limitation of iZ-C, living instance of Algorithm::CP::IZ must be only one per process.

# METHODS

create_int(INT)

Create an instance of Algorithm::CP::IZ::Int. Its domain contains INT.

create_int(VALUES [, NAME])

Create an instance of Algorithm::CP::IZ::Int. Its domain contains values specified by VALUES(arrayref).

create_int(MIN, MAX, [, NAME])

Create an instance of Algorithm::CP::IZ::Int. Its domain is {MIN..MAX}.

search(VARIABLES [, PARAMS])

Try to instantiate all VARIABLES(arrayref).

PARAMS will be hashref containning following keys.

FindFreeVar

FindFreeVar specifies variable selection strategy. Choose constants from Algorithm::CP::IZ::FindFreeVar or specify your own function as coderef here.

Most simple function will be following. (select from first)

``````    sub simple_find_free_var{
my \$array = shift; # VARIABLES is in parameter
my \$n = scalar @\$array;

for my \$i (0..\$n-1) {
return \$i if (\$array->[\$i]->is_free);
}

return -1; # no free variable
};``````
Criteria

Criteria specifies value selection strategy. Specify your own function as coderef here.

``````    sub sample_criteria {
# position in VARIABLES, and candidate value
my (\$index, \$val) = @_;

# first value used in search is
# minimum value returned by criteria.
return \$val;
};``````

(If ValueSelector is specified, this parameter is ignored.)

MaxFail

Upper limit of fail count while searching solutions.

ValueSelectors

Arrayref of Algorithm::CP::IZ::ValueSelector instances created via get_value_selector or create_value_selector_simple method.

(If ValueSelector is specified, this parameter is ignored.)

MaxFailFunc

CodeRef of subroutine which returns maxfail for restart.

NoGoodSet

A Algorithm::CP::IZ::NoGoodSet instance which collects NoGoods.

Notify

Specify a notify object receives following notification by search function.

``````    search_start
search_end
before_value_selection
after_value_selection
enter
leave
found``````

if OBJECT is a object, method having notification name will be called.

if OBJECT is a hashref, notification name must be a key of hash and value must be a coderef.

Returns 1 (success) or 0 (fail).

find_all(VARIABLES, CALLBACK [, PARAMS])

Find all solutions. CALLBACK(coderef) is called for each solution. (First parameter of CALLBACK is VARIABLE)

``````    # this callback collects all solutions in @r
my @r;
sub callback {
my \$var_array = shift;
push(@r, [map { \$_->value } @\$var_array]);
};``````

PARAMS will be hashref containning following keys.

FindFreeVar

Same as search method.

Returns 1 (success) or 0 (fail).

get_nb_fails

Returns fail count while searching solution.

get_nb_choice_points

Returns choice count while searching solution.

save_context

Save current status of variables and constraints.

``````  my \$v1 = \$iz->create_int(1, 9);
\$iz->save_context;    # current status is saved.
\$v1->Le(5);           # \$v1 is {1..5}
\$iz->restore_context; # \$v1 is restored to {1..9}``````

Returns integer which will be used for restore_context_until.

restore_context

Restore status of variables and constraints to last point which 'save_context' is called.

restore_context_until(LABEL)

Restore status of variables and constraints to point of label which 'save_context' returns.

restore_all

Restore status of variables and constraints to point of first 'save_context' call.

forget_save_context

Last save_context point is forgotten by calling this function.

forgest_save_context_until(LABEL)

save_context points until LABEL are forgotten by calling this function.

Cancel running search from other thread or signal handler. Context will be restored using restore_context_until if needed.

backtrack(VAR, INDEX, CALLBACK)

Set a callback function which will be called when context is restored to current status.

VAR is an instance of Algorithm::CP::IZ::Int.

INDEX is an integer value.

CALLBACK is a coderef which takes parameters like:

``````  sub callback {
# \$var = VAR, \$index = INDEX
my (\$var, \$index) = @_;
}``````
event_all_known(VARIABLES, CALLBACK, EXTRA)

Set a callback function which will be called when all variables in VARIABLES are instantiated.

VARIABLES is an arrayref contains instances of Algorithm::CP::IZ::Int.

CALLBACK is a coderef and takes parameters and must return like:

``````  sub callback {
# \$variables and \$extra are same as parameter.
my (\$variables, \$extra) = @_;

# return 1(success) or 0(fail)
return 1;
}``````

EXTRA is a just a data passed to callbeck as parameter (it can be anything).

event_known(VARIABLES, CALLBACK, EXTRA)

Set a callback function which will be called when any variable in VARIABLES is instantiated.

VARIABLES is an arrayref contains instances of Algorithm::CP::IZ::Int.

CALLBACK is a coderef and takes parameters and must return like:

``````  sub callback {
# \$val is instantited now.
# \$index is position in \$variables.
# \$variables and \$extra are same as parameter.
my (\$val, \$index, \$variables, \$extra) = @_;

# return 1(success) or 0(fail)
return 1;
}``````

EXTRA is a just a data passed to callbeck as parameter (it can be anything).

event_new_min(VARIABLES, CALLBACK, EXTRA)

Set a callback function which will be called when lower bound of any variable in VARIABLES is changed.

VARIABLES is an arrayref contains instances of Algorithm::CP::IZ::Int.

CALLBACK is a coderef and takes parameters and must return like:

``````  sub callback {
# minimum value of \$var is changed from \$old_min.
# \$var is same as \$variables[\$index].
# \$variables and \$extra are same as parameter.
my (\$var, \$index, \$old_min, \$variables, \$extra) = @_;

# return 1(success) or 0(fail)
return 1;
}``````

EXTRA is a just a data passed to callbeck as parameter (it can be anything).

event_new_max(VARIABLES, CALLBACK, EXTRA)

Set a callback function which will be called when upper bound of any variable in VARIABLES is changed.

VARIABLES is an arrayref contains instances of Algorithm::CP::IZ::Int.

CALLBACK is a coderef and takes parameters and must return like:

``````  sub callback {
# maximum value of \$var is changed from \$old_max.
# \$var is same as \$variables[\$index].
# \$variables and \$extra are same as parameter.
my (\$var, \$index, \$old_max, \$variables, \$extra) = @_;

# return 1(success) or 0(fail)
return 1;
}``````

EXTRA is a just a data passed to callbeck as parameter (it can be anything).

event_neq(VARIABLES, CALLBACK, EXTRA)

Set a callback function which will be called when value of any variable is removed in VARIABLES is changed.

VARIABLES is an arrayref contains instances Algorithm::CP::IZ::Int.

CALLBACK is a coderef and takes parameters and must return like:

``````  sub callback {
# \$val is removed from \$var.
# \$var is same as \$variables[\$index].
# \$variables and \$extra are same as parameter.
my (\$var, \$index, \$val, \$variables, \$extra) = @_;

# return 1(success) or 0(fail)
return 1;
}``````

EXTRA is a just a data passed to callbeck as parameter (it can be anything).

get_version

Returns version string like "3.5.0". undef will be returned if getVersion() is not supported in iZ-C (old version).

get_value_selector(ID)

Get built-in value selector (instance of Algorithm::CP::IZ::ValueSelector) specifed by ID. ID must be selected from following constants defined in package Algorithm::CP::IZ.

CS_VALUE_SELECTOR_MIN_TO_MAX
CS_VALUE_SELECTOR_MAX_TO_MIN
CS_VALUE_SELECTOR_LOWER_AND_UPPER
CS_VALUE_SELECTOR_UPPER_AND_LOWER
CS_VALUE_SELECTOR_MEDIAN_AND_REST

(These values are exported by Algorithm::CP::IZ and can be imported using tag 'value_selector')

Returned object will be used as a parameter ValueSelectors when calling "search" method.

``````  use Algorithm::CP::IZ qw(:value_selector);
my \$vs = \$iz->get_value_selector(CS_VALUE_SELECTOR_MIN_TO_MAX);

my \$v1 = \$iz->create_int(1, 9);
my \$v2 = \$iz->create_int(1, 9);
\$iz->Add(\$v1, \$v2)->Eq(12);
my \$rc = \$iz->search([\$v1, \$v2], {
ValueSelectors => [ \$vs, \$vs ],
});``````
create_value_selector_simple(CLASS_NAME)

Create user defined value-seelctor defined by class named CLASS_NAME. This class must have constructor named "new" and method namaed "next".

``````  use Algorithm::CP::IZ qw(:value_selector);

package VSSample1;
sub new {
my \$class = shift;
my (\$v, \$index) = @_;

my \$self = {
_pos => 0,
};
bless \$self, \$class;
}

sub next {
my \$self = shift;
my (\$v, \$index) = @_;

my \$pos = \$self->{_pos};
my \$domain = \$v->domain;

# return empty after enumerate all values
return if (\$pos >= @\$domain);

my @ret = (CS_VALUE_SELECTION_EQ, \$domain->[\$pos]);
\$self->{_pos} = ++\$pos;

# return pair of (CS_VALUE_SELECTION_*, value)
return @ret;
}

my \$v1 = \$iz->create_int(1, 9);
my \$v2 = \$iz->create_int(1, 9);
\$iz->Add(\$v1, \$v2)->Eq(12);
my \$vs = \$iz->create_value_selector_simple("VSSample1");
my \$rc = \$iz->search([\$v1, \$v2], {
ValueSelectors => [ \$vs, \$vs ],
});``````
create_no_good_set(VARIABLES, PRE_FILTER, MAX_NO_GOOD, EXT)

Create an instance of Algorithm::CP::IZ::NoGoodSet. Returned object will be used as a parameter NoGoodSet when calling "search" method.

# METHODS (Constraints)

Add(VAR1, VAR2 [, VAR3....])

Create an instance of Algorithm::CP::IZ::Int constrainted to be:

``  Created_instance  = VAR1 + VAR2 + ....``
Mul(VAR1, VAR2 [, VAR3....])

Create an instance of Algorithm::CP::IZ::Int constrainted to be:

``  Created_instance = VAR1 * VAR2 * ....``
Sub(VAR1, VAR2)

Create an instance of Algorithm::CP::IZ::Int constrainted to be:

``  Created_instance = VAR1 - VAR2``
Div(VAR1, VAR2)

Create an instance of Algorithm::CP::IZ::Int constrainted to be:

``  Created_instance = VAR1 / VAR2``
ScalProd(VARIABLES, COEFFICIENTS)

Create an instance of Algorithm::CP::IZ::Int constrainted to be:

``  Created_instance = COEFFICIENTS*VARIABLES + COEFFICIENTS*VARIABLES + ...``

VARIABLES is an arrayref contains instances of Algorithm::CP::IZ::Int, and COEFFICIENTS is an arreyref contains integer values.

AllNeq(VARIABLES)

Constraint all variables in VARIABLES to be different each other.

VARIABLES is an arrayref contains instances of Algorithm::CP::IZ::Int.

Returns 1 (success) or 0 (fail).

Sigma(VARIABLES)

Create an Algorithm::CP::IZ::Int instance constrainted to be:

``  Created_instance = VARIABLES + VARIABLES + ...``

VARIABLES is an arrayref contains instances of Algorithm::CP::IZ::Int.

Abs(VAR)

Create an instance of Algorithm::CP::IZ::Int constrainted to be:

``  Created_instance = abs(VAR)``
Min(VARIABLES)

Create an instance of Algorithm::CP::IZ::Int constrainted to be:

``  Created_value = minimum value of (VARIABLES, VARIABLES, ...)``

VARIABLES is an arrayref contains instances of Algorithm::CP::IZ::Int.

Max(VARIABLES)

Create an instance of Algorithm::CP::IZ::Int to be:

``  Created_instance = maximum value of (VARIABLES, VARIABLES, ...)``

VARIABLES is an arrayref contains instances of Algorithm::CP::IZ::Int.

IfEq(VAR1, VAR2, VAL1, VAL2)

Constraint VAR1 and VAR2 to be:

``````  VAR1 is instantiated to VAL1 and VAR2 is instantiated to VAL2.
VAR2 is instantiated to VAL2 and VAR1 is instantiated to VAL1.``````

Returns 1 (success) or 0 (fail).

IfNeq(VAR1, VAR2, VAL1, VAL2)

Constraint VAR1 and VAR2 to be:

``  pair (VAR1, VAR2) != pair (VAL1, VAL2)``

Returns 1 (success) or 0 (fail).

OccurDomain(VAL, VARIABLES)

Create instance of Algorithm::CP::IZ::Int represents count of VAL in VARIABLES.

VARIABLES is an arrayref contains instances of Algorithm::CP::IZ::Int.

OccurConstraints(VAR, VAL, VARIABLES)

Constraint VAR to represent count of VAL in VARIABLES.

VARIABLES is an arrayref contains instances of Algorithm::CP::IZ::Int.

Returns 1 (success) or 0 (fail).

Index(VARIABLES, VAL)

Create an instance of Algorithm::CP::IZ::Int represents position of VAL in VARIABLES.

``  VAL = VARIABLES[CREATED]``

VARIABLES is an arrayref contains instances Algorithm::CP::IZ::Int.

Element(VAR, VALUES)

Create an instance of Algorithm::CP::IZ::Int represents a value at VAR in VALUES. This relation is:

``  Created_instance = VALUES[VAR]``

VALUES is an arrayref contains integer values.

VarElement(VAR, VARIABLES)

Create an instance of Algorithm::CP::IZ::Int represents a value at VAR in VARIABLES. This relation is:

``  Created_instance = VARIABLES[VAR]``

VARIABLES is an arrayref contains instances of Algorithm::CP::IZ::Int.

VarElementRange(VAR, VARIABLES)

Create an instance of Algorithm::CP::IZ::Int represents a value at VAR in VARIABLES. This relation is:

``  Created_instance = VARIABLES[VAR]``

In contrast to VarElement, constraint propagation for variables in VARIABLES will occur only when upper or lower bound is changed.

VARIABLES is an arrayref contains instances of Algorithm::CP::IZ::Int.

Cumulative(START_VARS, DURATION_VARS, RESOUCE_VARS, LIMIT_VAR)

Constraint variables as "Cumulative".

START_VARS, DURATION_VARS and RESOUCE_VARS are an arrayref contains instances of Algorithm::CP::IZ::Int and LIMIT_VAR is an instance of Algorithm::CP::IZ::Int.

Disjunctive(START_VARS, DURATION_VARS)

Constraint variables as "Disjunctive".

START_VARS and DURATION_VARS are an arrayref contains instances of Algorithm::CP::IZ::Int.

ReifEq(VAR1, VAR2)

Create an instance of Algorithm::CP::IZ::Int represents state of VAR1 == VAR2. Created variable will be instantiated to 1 when VAR1 == VAR2 otherwise to 0.

ReifNeq(VAR1, VAR2)

Create an instance of Algorithm::CP::IZ::Int represents state of VAR1 != VAR2. Created variable will be instantiated to 1 when VAR1 != VAR2 otherwise to 0.

ReifLt(VAR1, VAR2)

Create an instance of Algorithm::CP::IZ::Int represents state of VAR1 < VAR2. Created variable will be instantiated to 1 when VAR1 < VAR2 otherwise to 0.

ReifLe(VAR1, VAR2)

Create an instance of Algorithm::CP::IZ::Int represents state of VAR1 <= VAR2. Created variable will be instantiated to 1 when VAR1 <= VAR2 otherwise to 0.

ReifGt(VAR1, VAR2)

Create an instance of Algorithm::CP::IZ::Int represents state of VAR1 > VAR2. Created variable will be instantiated to 1 when VAR1 > VAR2 otherwise to 0.

ReifGe(VAR1, VAR2)

Create an instance of Algorithm::CP::IZ::Int represents state of VAR1 >= VAR2. Created variable will be instantiated to 1 when VAR1 >= VAR2 otherwise to 0.

# AUTHOR

Toshimitsu FUJIWARA, <tttfjw at gmail.com>

# COPYRIGHT AND LICENSE

Copyright (C) 2015 by Toshimitsu FUJIWARA

This program is free software; you can redistribute it and/or modify it under the terms of the the Artistic License (2.0). You may obtain a copy of the full license at:

http://www.perlfoundation.org/artistic_license_2_0

Any use, modification, and distribution of the Standard or Modified Versions is governed by this Artistic License. By using, modifying or distributing the Package, you accept this license. Do not use, modify, or distribute the Package, if you do not accept this license.

If your Modified Version has been derived from a Modified Version made by someone other than you, you are nevertheless required to ensure that your Modified Version complies with the requirements of this license.

This license does not grant you the right to use any trademark, service mark, tradename, or logo of the Copyright Holder.

This license includes the non-exclusive, worldwide, free-of-charge patent license to make, have made, use, offer to sell, sell, import and otherwise transfer the Package with respect to any patent claims licensable by the Copyright Holder that are necessarily infringed by the Package. If you institute patent litigation (including a cross-claim or counterclaim) against any party alleging that the Package constitutes direct or contributory patent infringement, then this Artistic License to you shall terminate on the date that such litigation is filed.

Disclaimer of Warranty: THE PACKAGE IS PROVIDED BY THE COPYRIGHT HOLDER AND CONTRIBUTORS "AS IS' AND WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES. THE IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, OR NON-INFRINGEMENT ARE DISCLAIMED TO THE EXTENT PERMITTED BY YOUR LOCAL LAW. UNLESS REQUIRED BY LAW, NO COPYRIGHT HOLDER OR CONTRIBUTOR WILL BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES ARISING IN ANY WAY OUT OF THE USE OF THE PACKAGE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.